About the Sequence aplet | HP 39g+ Graphing instruction

6

Sequence aplet

About the Sequence aplet

The Sequence aplet allows you to explore sequences.

You can define a sequence named, for example, U1:

•in terms of n

•in terms of U1(n–1)

•in terms of U1(n–2)

•in terms of another sequence, for example, U2(n)

•in any combination of the above.

The Sequence aplet allows you to create two types of graphs:

–A Stairsteps graph plots n on the horizontal axis and Un on the vertical axis.

–A Cobweb graph plots Un–1on the horizontal axis and Un on the vertical axis.

Getting started with the Sequence aplet

Open the Sequence aplet

The following example defines and then plots an expression in the Sequence aplet.

1. Open the Sequence aplet.

Select

Sequence

The Sequence aplet starts in the Symbolic view.

Sequence aplet

6-1

Image 81

HP 39g+ Graphing manual About the Sequence aplet, Getting started with the Sequence aplet

Contents

Edition Part Number F2224-90001 User’s guide Edition December Printing History Contents Plotting a piecewise-defined function Using variables in equationsAbout the Solve aplet Getting started with the Polar aplet One-Proportion Z-Interval Confidence intervals One-Sample Z-Interval10-7 11-1 Variables and memory management 16-2 16-1Creating and editing programs 16-4 16-7 Service Regulatory information Glossary Resetting the hp 39g+Operating details Variables Home variables Manual conventions PrefaceHewlett Packard’s Calculators web site can be found at Function, Polar, Parametric Preface To cancel On/off, cancel operationsGetting started To turn on Display To adjustParts of the display Contrast Keyboard Menu keysInfrared or cable Displays the Aplet Library menu. See Aplet library on Aplet control keys Entry/Edit keys SameButton performs Shifted keystrokes Math keys Helpwith Menus CommandsProgram Inactive keys Input forms Reset input form values You use the Modes input form to set the modes for Home Mode settingsCurrent aplet and Home give Same result Function arguments. Comma mode Setting Options NumberLists and matrices, and to separate Uses periods dot as separators Setting a mode Aplets E-lessonsPress to return to Home Polar Example x = cost and y = sintSequence Sequence functions U in terms of n, or Another sequence, such as Un 1 Quad Explorer aplet Keys Transforms Graph, with these Amplitude and frequencySeen by experimenting Symbolic view Aplet libraryAplet views Plot view Numeric view Plot-Table view Plot-Detail view Select Plot-TableSelect Plot-Detail Plot Setup Aplet view configurationOverlay Plot view Sketch view Views menu contains the Overlay Plot view Where to start Numeric Setup Symbolic SetupMathematical calculations Entering expressions Long results Negative numbers Scientific notation powers Using23 3 EEX Explicit and implicit multiplication ParenthesesEntering Calculates Sin 45 + π Input Output Last input Edit line Last output Getting started Storing a value in a variable Using fractions Accessing the display history Clearing the display historySetting Fraction mode Setting fraction precision Fraction calculations SelectFraction Converting decimals to fractions Complex numbers Catalogs and editors Defining an expression Symbolic view About the Symbolic viewAplets and their views Aplet views U0. Define the nth term Independent variable in the expressions is T Evaluating expressions ApletsSelect Function Home About the Plot view Setting up the plot Plot view setup Plot view settings ΘRNGΘSTEP Exploring the graph Reset plot settings To move between relations Trace a graph Zoom within a graph To jump directly to a value To turn trace on/offZoom options Set SquareFactors Auto Scale Now un-zoom Un-zoom Box Zoom option lets you draw a box around To box zoomOne diagonal of the zoom rectangle To turn on the menu-key Press to zoom in on the boxed area Views menu options Other views for scaling and splitting the graph Split the screen Pixel=π/24 radian, 7.58, orPress or About the numeric view Numeric view settings Setting up the table Numeric view setup Exploring the table of numbers NUM view menu keys Zoom within a tableNumstart and Numstep Building your own table of numbers Build a tableNumtype Build Your Own Clear data Build Your Own menu keys Example plotting a circle Reset the graph setup to the default settingsPlot the circle, x 2+ y 2 = 9. First rearrange it to read Function aplet, specify the functions Display the functions in numeric form About the Function aplet Function apletGetting started with the Function aplet Open the Function aplet Plot the functions Define the expressions Set up the plotSpecify a grid for the graph Plot the functions Select Auto Change the scale Trace a graphScale Times Select Root Analyse graph with FCN functions Select Signed area Select Slope Select Extremum To find the extremum of the quadratic Display the numeric view Explore the tableDisplay the table of values Display the symbolic definition for the F1 column Symbolic definition A columnSymbolic definition F1 is displayed at Bottom of the screen To display Function aplet interactive analysis Select Plot FCNOr to choose a variable Root FCN functionsExtremum Slope Shading area Symbolic view. DisplaysIntersection Cursor. You need to have at Plotting a piecewise-defined function About the Parametric aplet Parametric apletGetting started with the Parametric aplet Define the expressions Set angle measure Set up the plot Plot the expressionSet the angle measure to degrees Select Degrees Overlay plot Display the numbers Plot a triangle graph over the existing circle graph120 Page Getting started with the Polar aplet Polar apletOpen the Polar aplet Select Polar Display the Plot view menu key labels Explore the graph Display the numbers Sequence aplet Sequence aplet starts in the Symbolic viewAbout the Sequence aplet Getting started with the Sequence aplet Menu keys to assist in the entry of equations Plot Setup, set the Seqplot option to Cobweb Display the . Display the table of values for this example Select CobwebPage About the Solve aplet Solve aplet Open the Solve aplet Getting started with the Solve apletDefine the equation Enter known variables Select Solve Solve the unknown variable Plot the equation Select Auto Scale Use an initial guess Interpreting results Consider the equation of motion for an accelerating body Plotting to find guesses Plot the graph To highlight T Press until the cursor is at the intersection Using variables in equations Statistics aplet About the Statistics apletGetting started with the Statistics aplet Enter data Select StatisticsTo move to the next column Choose fit and data columns Explore statistics Select a fit in the Symbolic setup viewSelect Linear Value is Display the equation for best linear fit Setup plot Plot the graph Draw the regression curveTo move to the FIT1 field Slope m is 425.875. The y-intercept b is To highlight Predict values Statistics aplet’s Numeric view keys are Entering and editing statistical data Statistics Variable expression to the edit line Copies the column variable or Clear is used Data sets will need to be selectedAgain before re-use Plot a histogram of the data Save data Sort data values Edit a data set Delete data Insert data Defining a regression model Angle SettingTo choose the fit Fit models To define your own fit Computed statistics Two-variable 7,8,15,16,17ΣX2 Plotting To plot statistical dataColumns for a linear fit only Histogram Box and Whisker Plot Scatter Plot Plot types Relative Error Fitting a curve to 2VAR dataCorrelation coefficient Setting up the plot Plot setup view Trouble-shooting a plotHistogram range Plotting mark 2VAR Connected points 2VAR Erases the plot Statistics aplet’s Plot view keys Find predicted values Calculating predicted values Statistics aplet Page About the Inference aplet Inference apletGetting started with the Inference aplet Open the Inference aplet Inference aplet’s Symb view keys Table below summarizes the options available Symbolic view Select the inferential method Enter data Setup-NUMSelect Hypoth Test Test 1 ∝ Importing sample statistics from the Statistics aplet Are explained in the feature of this aplet Statistics aplet opens in the Numeric view If the Decimal Mark setting in the Modes input formC1 column, enter the random numbers Produced by the calculator 529 295 952 259 925 592 Open Inference aplet Set up the interval calculationInference Select Conf Interval Display Numeric view Display Plot view Specify a 90% Confidence interval in the C fieldTo move to the C field One-Sample Z-Test Hypothesis testsMenu name Inputs Results Two-Sample Z-Test Population 2 standard One-Proportion Z-TestTest 1π Measures the strength of the evidence for a selected Two-Proportion Z-Test One-Sample T-Test With the α level that you Sample standard deviation Pooled? Two-Sample T-Test One-Sample Z-Interval Confidence intervals Two-Sample Z-Interval Two-Proportion Z-Interval One-Proportion Z-Interval One-Sample T-Interval Pooled Two-Sample T-Interval Critical T Critical value for T Background Using the Finance Solver 3 4 Compounding period -- which is Performing TVM calculations Soft menu key. The resulting value is PV = $15,705.85 Example 1 Loan calculations Example 2 Mortgage with balloon payment To calculate amortizations Calculating AmortizationsExample 3 Amortization for home mortgage To continue amortizing the loan Example 4 Amortization for home mortgage Math functions Using mathematical functionsMath menu Name. Note You do not need to press first Function categories Math functions by categorySyntax Functions common to keyboard and menus Value1+ value2 , etc Keyboard functionsEvalue E5 returns LOG100 returns Returns ABS1,2 returns Nthroot 8 returns Calculus functions∂ s1s1 2+3*s1 returns 2*s1+3 S1,2*X+3,X Taylor Complex number functionsARG Conj Hyperbolic trigonometry Constants Loop functions List functions Polynomial functions Matrix functionsPolycoef POLYCOEF2,-3,4,-5 returns1,2,-25 Polyeval PolyformPolyroot Comb Probability functionsPerm Random Real-number functions Frac FnrootHMS→ →HMS MIN MAXMOD Change Round Two-variable statisticsSign Truncate Isolate Symbolic functionsLINEAR? Quad Quote Test functions Trigonometry functions Using formal variables Symbolic calculationsSEC SECvalue Symbolic calculations in the Function aplet Finding derivativesTo find derivatives in Home Show the result To find derivatives in the Function aplet’s Symbolic viewSelect F2X and evaluate it You could also just define To find the indefinite integral using formal variables For example, to find the indefinite integralThus, substituting X for S1, it can be seen that 11-24 Introduction Variables and memory management Storing and recalling variables Calculations To use variablesYou can use variables in calculations. The calculator Substitutes the variable’s value in the calculation Open the Vars menu Vars menuPress Move the highlight to the variables column Names or values of variables into programs Add the contents of two list variables, and to storeExample Result in another list variable 12-6 Real part, and i represents That you can configure usingVariable on page 15-5 for more Information on storing graphic object via X0, Y0 to X9, Y9 Symbolic view. See To access an apletVariable Aplet variables on page R-7 Line, press and press Memory ManagerPage Vectors MatricesMatrices Matrix Variables Creating and storing matrices Matrix Catalog keysPOLYROOT1,0,-1,0XM1 To create a matrix in the Matrix Catalog Working with matrices To transmit a matrixOr column you are prompted to Make a choice If M2 is 3,4,5,6, then M21,2 returns Key Meaning Moves to the first row, last row, first Matrix arithmetic To store one elementCreate the second matrix Matrices 13-7 Solving systems of linear equations To negate eachElement Matrix functions and commands About functionsSelect Real matrix Colnorm Argument conventionsCond Cross DOT DETEigenval Eigenvv Rownorm RankRref Schur SVD ExamplesSVL Trace Following set of equations x 2y + 3z = 14 2x + y z = Reduced-Row Echelon Form You can create, edit, delete, send, and receive named Lists List catalog keys List edit keys Create a list To display a list Displaying and editing listsTo display one To edit a list To insert an element 1. Open the List catalog A listPress , and press 148 L12 Deleting lists List functionsTransmitting lists To delete a list CONCATlist1,list2 2,3 returns 5,10,15CONCAT1,2,3,4 returns 1,2,3,4 ∆LISTlist1 ΠLIST2,3,4 returns ΠLISTlistPOSlist, element POS 3, 7, 12, 19,12 returns ΣLIST2,3,4 returns Finding statistical values for list elementsSorts elements in ascending order. SORTlist List, L1 Create L1 with values 88, 90, 89, 65, 70, Are now in column 1 C1 To write a note in Note view Aplet note viewYour work is automatically saved. Press any view key Or to exit the Notes view Commands Contents of variablesSpace key for text entry Alpha-lock for letter entry Aplet sketch view Sketch keysTo draw a line Draw keys To draw a box Press to continue drawing, or press Mynote Begins a new note, and asks Opens the selected note forFor a name Another hp 39g+ or PC Press instead Programming Contents of a Program Structured Programming Open Program Catalog Program catalogBe simple-or it can be divided further into other Programs that perform smaller tasks Program catalog keys Creating and editing programs Create a new programPress Progrm to open the Program catalog On the left, use or to highlight a command Press to paste the command into the program editorEdit a program 1. Press Progrm to Editing keys Run a program Debug a program Stop a program Using programs Transmit a program Customizing an aplet Example Aplet naming convention Save the aplet Configuring the Setviews menu option programs ’’My Entry1’’’’EXP.ME1’’1 Setviews ’’’’ ’’’’18’’My Entry2’’’’EXP.ME2’’3 ’’ ’’’’EXP.SV’’0 Programming commands ’’’’’’EXP.ANG’’0’’START’’’’EXP.S’’7 Check Aplet commandsSelect Setviews Auto-run programs Associating programs with your aplet ProgramName ViewNumberIncluding standard menu options IF...THEN...END Branch commandsUncheck n 1XA IF... THEN... Else Iferr trap-clause Then error-clause ENDEND CASE...END Iferr Then END RUN Drawing commandsStop ARC Graphic commands →GROB →DISPLAYGrobnot Grobor Do a + 1 X a Until a == Loop commands Matrix commands Delrow DelcolEditmat Randmat Prompt commands Print commands Disp ChooseDisptime Disp 3A is 2+2 Getkey Input nametitle,labelhelpdefaultInput Editmat matrixname Msgbox Stat-One and Stat-Two commandsPrompt Wait Stat-Two commands Stat-One commands Plot-view variables Storing and retrieving variables in programsArea Axes Extremum CoordFastRes Grid Indep HwidthInvCross Isect Recenter Nmin / NmaxRoot S1mark-S5mark Slope SimultStatPlot Umin/Umax Tracing Tmin / TmaxTstep Xcross Ytick XtickXmin / Xmax Ymin / Ymax Symbolic-view variables U1...U9, U0 R1...R9, R0E1...E9, E0 S1fit...S5fit C1...C9, C0 Numeric-view variablesDigits Format NumFont NumColNumIndep NumRow NumType NumStepNumZoom StatMode PageNum Sketch variablesGraphicname X PageNum Creating new aplets based on existing aplets Extending aplets Open the Solve aplet and save it under the new name SolveDegrees Resetting an aplet Using a customized apletChoose the sine formula in E1 Downloading e-lessons from the web Sending and receiving apletsHewlett-Packard’s Calculators web site can be found at To transmit an aplet Sorting items in the aplet library menu list To sort the aplet list To delete an aplet Glossary Reference informationExpression line# Cross matrix1,matrix2 Record using the Program editor Editor and catalog Matrix Two-dimensional array of valuesVector One-dimensional array of values Set to Comma and enclosed To erase all memory and reset defaults Resetting the hp 39g+To reset using the keyboard Split screens Operating details If the calculator does not turn onBatteries To install the main batteries To install the backup battery Home variables Variables Function aplet variables Area Root Extremum Slope IsectAngle Parametric aplet variables are Category Available name Plot Parametric aplet variables Polar aplet variables are Category Available names Plot Polar aplet variables Sequence aplet variables are Category Available name Plot Sequence aplet variables Solve aplet variables Solve aplet variables are Category Available name PlotDigits NumCol Format NumRow Statistics aplet variables Math functions Math menu categoriesMath functions are Category Available name Calculus Hyperb Polynom Category Available name Matrix Program constants Program commands are Category Command Aplet Program commandsBranch Print Status messages Or intersection is not visible Function value, root, extremumCurrent screen Such as 0/0 Hp 39g+ Graphing Calculator Warranty period 12 months Limiting Warranty Limiting Warranty Service Rotc = Rest of the country Canada 905 206-4663 or USA Regulatory information Limiting Warranty Index Maximum real number 11-8 minimum real number Freeze 16-20 Line 16-20 Pixoff 16-20 Pixon 16-20 Tline Grobxor Grobor Inverse hyperbolic cosine 11-8 inverse hyperbolic functions Break Angle measure 1-10 decimal mark 1-11 number format Order of precedence 1-21 overlaying plots 2-16,4-3 11-8 Sending and receiving 16-8 structured Menu lists 1-8 speed searches Navigate around 3-8 numeric values 3-7 numeric view setup Index